Eisner-Choi-Diaz-O’Neill-Trafford Calcium map

This model is used to simulate Calcium Alternans.

While electrical alternans can be atributed to cellular electrical currents and in some cases to dynamics associated with the APD restitution curve, alternans also can result from intracellular calcium dynamics. The calcium and membrane potential dynamics in cardiac cells are two coupled systems, as the shape of the action potential is determined by ionic currents across the cell membrane, and some of these currents are dependent on the intracellular calcium concentrations that may in turn depend on the membrane potential. It has been shown that during rapid pacing the intracellular calcium concentration can alternate even while the action potential shape, and thus its duration, is held constant[1]. One mechanism known to produce alternans in the intracellular cytoplasmic calcium concentration (calcium transient) is the nonlinear relation between the calcium fluxes across the sarcolemma and the sarcoplasmic reticulum (SR) content[2]. The applet above shows how alternans and other complex rhythms can appear when there is a steep relationship between the SR content and the calcium efflux, using the Eisner-Choi-Diaz-Neill-Trafford map of intracellular calcium dynamics:

This is a classical negative fedback system where N is a Hill coefficient that represents the nonlinearity of the system. This relationship includes the dependence of calcium release on SR content, the calcium buffering properties of the cytoplasm, and the relationship between the calcium transient and calcium efflux. At low values of N the sytem is stable; however, as N increases above 5 the relation becomes steep enough to produce alternans.

[1]Intracellular Ca2+ Dynamics and the Stability of Ventricular Tachycardia E. Chudin, J. Goldhaber, A. Garfinkel, J. Weiss, and B. Kogan; Biophys J, December 1999, p. 2930-2941, Vol. 77, No. 6
[2] Integrative Analysis of Calcium Cycling in Cardiac Muscle. DA Eisner, HS Choi, ME Diaz, S.C. O’Neill, AW Trafford Circ Res 2000, 87:1087-1094